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# Recent Differential equations Answers # Recent questions in Differential equations

First order differential equations asked 2021-03-02

### Solve differential equation $$ty'+(t+1)y=t, y(ln 2)=1$$, t>0

First order differential equations asked 2021-03-02

### Solve the differential equation $$(x-3y)dx-xdy=0$$

First order differential equations asked 2021-03-02

### Transform the given initial value problem into an initial value problem for two first-order quations $$u"+0.25u'+4u=2cos(3t)$$, u(0)= 1, u'(0)= -2

First order differential equations asked 2021-03-01

### Solve differential equation $$t^2dy= (8ln^2t-ty)dt$$

Laplace transform asked 2021-02-26

### Solve the following initial value problems using Laplace Transforms: $$\displaystyle\frac{{{d}^{2}{y}}}{{{\left.{d}{x}\right.}^{2}}}+{25}{y}={t}$$ $$y(0)=0$$ $$y'(0)=0.04$$

Laplace transform asked 2021-02-26

### How many poles does the Laplace Transform of a square wave have? a) 0 b) 1 c) 2 d) Infinitely Manhy

Differential equations asked 2021-02-26

### Make and solve the given equation $$x\ dx\ +\ y\ dy=a^{2}\frac{x\ dy\ -\ y\ dx}{x^{2}\ +\ y^{2}}$$

First order differential equations asked 2021-02-25

### Solve differential equation $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}+{\frac{{{y}}}{{{4}{x}}}}={3}{x},\ {y}{\left({2}\right)}={3}$$

Second order linear equations asked 2021-02-25

### Solve the linear equations by considering y as a function of x, that is, y = y(x). $$\displaystyle\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}-{y}={4}{e}^{x},{y}{\left({0}\right)}={4}$$

Laplace transform asked 2021-02-25

### Use properties of the Laplace transform to answer the following (a) If $$f(t)=(t+5)^2+t^2e^{5t}$$, find the Laplace transform,$$L[f(t)] = F(s)$$. (b) If $$f(t) = 2e^{-t}\cos(3t+\frac{\pi}{4})$$, find the Laplace transform, $$L[f(t)] = F(s)$$. HINT: $$\cos(\alpha + \beta) = \cos(\alpha)\cos(\beta) - \sin(\alpha) \sin(\beta)$$ (c) If $$F(s) = \frac{7s^2-37s+64}{s(s^2-8s+16)}$$ find the inverse Laplace transform, $$L^{-1}|F(s)| = f(t)$$ (d) If $$F(s) = e^{-7s}(\frac{1}{s}+\frac{s}{s^2+1})$$ , find the inverse Laplace transform, $$L^{-1}[F(s)] = f(t)$$

Laplace transform asked 2021-02-25

### Solve no.4 inverse laplace $$L^{-1}\left\{s \ln\left(\frac{s}{\sqrt{s^2+1}}\right)+\cot^{-1s}\right\}$$

Differential equations asked 2021-02-25

### Give the correct answer and solve the given equation: $$\displaystyle{y}\ \text{ - 4y}+{3}{y}={x},{y}_{{1}}={e}^{x}$$

Laplace transform asked 2021-02-24

### For the function $$f(t)=e^t$$ $$g(t)=e^{-2t}$$ $$0\leq t < \infty$$ compute in two different ways: a) By directly evaluating the integral in the defination of $$f \cdot g$$ b) By computing $$L^{-1}\left\{F(s)G(s)\right\} \text{ where } F(s)=L\left\{f(t)\right\} \text{ and } G(s)=L\left\{g(t)\right\}$$

Second order linear equations asked 2021-02-24

### Solve the linear equations by considering y as a function of x, that is, y = y(x). $$\displaystyle\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}+{\left(\frac{1}{{x}}\right)}{y}={x}$$

Laplace transform asked 2021-02-24

### determine the inverse Laplace transform of F. $$F(s)=\frac{e^{-2s}}{(s-3)^3}$$

Laplace transform asked 2021-02-24

### What would be the laplace transform of a function of f or $$L\left\{f(t)\right\}$$?

First order differential equations asked 2021-02-24

### Solve the differential equation $$x dy/dx= y+xe^(y/x)$$, y=vx

First order differential equations asked 2021-02-24

### Solve differential equation $$(x+2)y′+4y=(3x + 6)^-2 lnx$$

First order differential equations asked 2021-02-23

### Solve differential equation $$dy/dx+ycos(x)= 4cos(x)$$, y(0)=6

First order differential equations asked 2021-02-21

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